Functional characterizations of trace spaces in Lipschitz domains

Abstract

Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces Hs(∂Ω) involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary ∂Ω of a bounded Lipschitz domain Ω⊂Rd and applying Moore–Penrose pseudoinverse properties together with a special inner product on H1(Ω). We also establish generalized results of the Moore–Penrose pseudoinverse.